FRANTIC: A Fast Reference-based Algorithm for Network Tomography via compressive sensing

We study the problem of link and node delay estimation in undirected networks when at most k out of n links or nodes in the network are congested. Our approach relies on end-to-end measurements of path delays across pre-specified paths in the network. We present a class of algorithms that we call FRANTIC. The FRANTIC algorithms are motivated by compressive sensing; however, unlike traditional compressive sensing, the measurement design here is constrained by the network topology and the matrix entries are constrained to be positive integers. A key component of our design is a new compressive sensing algorithm SHO-FA-INT that is related to the SHO-FA algorithm [1] for compressive sensing, but unlike SHO-FA, the matrix entries here are drawn from the set of integers {0, 1, ...,M}. We show that O(k log n/log M) measurements suffice both for SHO-FA-INT and FRANTIC. Further, we show that the computational complexity of decoding is also O(k log n/log M) for each of these algorithms. Finally, we look at efficient constructions of the measurement operations through Steiner Trees.